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Beliebt Rechnen >

integral of (1-0.4x)/((1-x)(5-x))

Lösung

\int \frac{1 - 0.4 x}{( 1 - x ) ( 5 - x )} d x

Lösung

- 0.15 ln ∣ x - 1 ∣ - 0.25 ln ∣ x - 5 ∣ + C

Schritte zur Lösung

\int \frac{1 - 0.4 x}{( 1 - x ) ( 5 - x )} d x

Ermittle den Partialbruch von

\frac{1 - 0.4 x}{( 1 - x ) ( 5 - x )} : - \frac{0.15}{x - 1} - \frac{1}{4 ( x - 5 )}

= \int - \frac{0.15}{x - 1} - \frac{1}{4 ( x - 5 )} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{0.15}{x - 1} d x - \int \frac{1}{4 ( x - 5 )} d x

\int \frac{0.15}{x - 1} d x = 0.15 ln ∣ x - 1 ∣

\int \frac{1}{4 ( x - 5 )} d x = \frac{1}{4} ln ∣ x - 5 ∣

= - 0.15 ln ∣ x - 1 ∣ - \frac{1}{4} ln ∣ x - 5 ∣

Vereinfache

= - 0.15 ln ∣ x - 1 ∣ - 0.25 ln ∣ x - 5 ∣

Füge eine Konstante zur Lösung hinzu

= - 0.15 ln ∣ x - 1 ∣ - 0.25 ln ∣ x - 5 ∣ + C

Graph

Beliebte Beispiele

integral from-infinity to infinity of t

\int_{- \infty}^{\infty} t d t

derivative of (5-(4-3x^2)^3)

\frac{d}{d x} ((5 - (4 - 3 x)^{2})^{3})

(dy)/(dx)=a^{x+y}

\frac{d y}{d x} = a^{x + y}

integral of x^4tan^3(x^5)

\int x^{4} tan^{3} (x^{5}) d x

integral of sinh(5x)

\int sinh (5 x) d x